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Flows in Complex Systems

Control of Flow Separation Around Bluff Obstacles by Transverse Magnetic Field

[+] Author and Article Information
Dipankar Chatterjee1

 Simulation and Modeling Laboratory, CSIR-Central Mechanical Engineering Research Institute, Durgapur-713209, India e-mail: d_chatterjee@cmeri.res.in Department of Mechanical Engineering, Dr. B. C. Roy Engineering College, Durgapur-713206, India;   National Institute of Technology Durgapur, Durgapur-713209, India Simulation and Modeling Laboratory, CSIR-Central Mechanical Engineering Research Institute, Durgapur-713209, India

Kanchan Chatterjee, Bittagopal Mondal

 Simulation and Modeling Laboratory, CSIR-Central Mechanical Engineering Research Institute, Durgapur-713209, India e-mail: d_chatterjee@cmeri.res.in Department of Mechanical Engineering, Dr. B. C. Roy Engineering College, Durgapur-713206, India;   National Institute of Technology Durgapur, Durgapur-713209, India Simulation and Modeling Laboratory, CSIR-Central Mechanical Engineering Research Institute, Durgapur-713209, India

1

Corresponding author.

J. Fluids Eng 134(9), 091102 (Aug 21, 2012) (11 pages) doi:10.1115/1.4007316 History: Received May 21, 2012; Revised July 31, 2012; Published August 21, 2012; Online August 21, 2012

Electromagnetic fields may be used to control the flow separation during the flow of electrically conducting fluids around bluff obstacles. The steady separated flow around bluff bodies at low Reynolds numbers almost behaves as a creeping flow at a certain field strength. This phenomena, although already known, is exactly quantified through numerical simulation and the critical field strength of an externally applied magnetic field is obtained, for which the flow separation is completely suppressed. The flow of a viscous, incompressible, and electrically conducting fluid (preferably liquid metal or an electrolyte solution) at a Reynolds number range of 10–40 and at a low magnetic Reynolds number is considered in an unbounded medium subjected to uniform magnetic field strength along the transverse direction. Circular and square cross sections of the bluff obstacles are considered for simulation purposes. Fictitious confining boundaries are chosen on the lateral sides of the computational domain that makes the blockage ratio (the ratio of the cylinder size to the width of the domain) 5%. The two-dimensional numerical simulation is performed following a finite volume approach based on the semi-implicit method for pressure linked equations (SIMPLE) algorithm. The major contribution is the determination of the critical Hartmann number for the complete suppression of the flow separation around circular and square cylinders for the steady flow in the low Reynolds number laminar regime. The recirculation length and separation angle are computed to substantiate the findings. Additionally, the drag and skin friction coefficients are computed to show the aerodynamic response of the obstacles under imposed magnetic field conditions.

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Figures

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Figure 1

Schematic diagram of the computational domain. The external magnetic field (B0 ) is applied along the transverse (y) direction.

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Figure 2

Typical grids used for simulation (expanded view around the cylinders)

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Figure 3

Schematic of the wake bubble geometry for (a) circular, and (b) square cylinders

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Figure 4

(a),(b) Variation of dimensionless bubble length (Lr ), (c) separation angle (φ), (d) bubble width (W), (e),(f) overall drag coefficient (CD ) with Reynolds number (Re) for Ha = 0 (without magnetic field) for circular and square cylinders

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Figure 5

Streamlines around the cylinders for Ha = 0 (no magnetic field) at different Reynolds numbers

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Figure 6

Streamlines around te circular cylinder for Re = 20 at different Hartmann numbers

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Figure 7

Streamlines around the circular cylinder for Re = 40 at different Hartmann numbers

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Figure 8

Streamlines around the square cylinder for Re = 20 at different Hartmann numbers

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Figure 9

Streamlines around the square cylinder for Re = 40 at different Hartmann numbers

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Figure 10

Critical Hartmann number as a function of the Reynolds number for circular and square cylinders

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Figure 11

Variation of the recirculation length with the Hartmann number for (a) circular, and (b) square cylinders at different Reynolds numbers

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Figure 12

Variation of the separation angle with the Hartmann number for (a) circular, and (b) square cylinders at different Reynolds numbers

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Figure 13

Variation of the drag coefficient with the Hartmann number at different Reynolds numbers for (a) circular, and (b) square cylinders

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Figure 14

Skin friction coefficient at the rear stagnation point as a function of the Hartmann number at a fixed Reynolds number for circular and square cylinders

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